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Unformatted text preview: rom all the newspapers printed during a single day. In this sample,
35 contain some type of nonconforming attribute. Construct and
interpret a 90% confidence interval for the proportion of newspapers
printed during the day that have a nonconforming attribute. To Try…
5. Management wants an estimate of the proportion of the corporation’s
employees who favour a bonus plan. From a random sample of 344
employees, it was found that 261 were in favour of this particular
plan. Find a 90% confidence interval estimate of the population
proportion that favours this modified bonus plan. p
α=.10; zα/2 = z0.05 =1.645;
Confidence interval:
p ± zα 2 p( − p)
1
n = 261/344 = 0.7587; n = 344
Sample:
344 proportion pbar: 0.75872093 significance α: 0.1 confidence: 0.7587⋅ 0.2413
344
0.7587 ± 0.0379 size n: 90% standard error of the proportion: 0.023068621 0.7587 ± 1.645 Interval Estimation Sampling Distribution: 0.7208 ≤ p ≤ 0.7966 Or using MS Excel: Interval Estimate: Lower: =.7587–
NORM.S.INV(1–.10/2)*SQRT(.7587*(1–.7587)/344)=0.720754373 zα/2: 1.644853627 margin of error: 0.037944505 To Try…
The operations manager at a large newspaper wants to estimate the
proportion of newspapers printed that have a nonconforming attribute (e.g.,
excessive ruboff, improper page setup, missing or duplicate pages). A
random sample of 200 newspapers is selected from all the newspapers
printed during a single day. In this sample, 35 contain some type of
nonconforming attribute. Construct and interpret a 90% confidence interval
for the proportion of newspapers printed during the day that have a
nonconforming attribute.
p
α=.10; zα/2 = z0.05 =1.645; = 35/200 = 0.175; n = 200 6. Confidence interval:
p ± zα 2 p (1− p)
n Sample:
size n: 200 proportion pbar: 0.175 significance α: 0.1 confidence: 90% Lower: =.175–
Interval Estimate:
NORM.S.INV(1–.10/2)*SQRT(.175*(1–.175)/200)=0.130806514
standard error of the proportion: 0.026867732 0.175 ± 1.645 0.175⋅0.825
200 Interval Estimation 0.175 ± 0.0442
0.1308 ≤ p ≤ 0.2192 Sampling Distribution: Or using MS Excel: Upper: zα/2: 1.644853627...
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 Spring '13

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